1. Field of the Invention
The present invention relates generally to methods and systems for computing the function value of a point using interpolation on known or measured function values of neighboring points, and more particularly to methods and systems for multi-dimensional interpolation for color space conversion.
2. Description of Related Art
The need for multi-dimensional interpolation arises in many fields of signal and image processing, where it is required to determine the function value of a point in multi-dimensional space based on the known function values of a set of other points. A point with a known function value is usually called a “node”. However, for simplicity, hereinafter, the terms “point” and “node” will be used interchangeably, and the term “known node” will be used to denote a point with a known function value. Traditionally, in many applications, the known nodes are conveniently selected to be at fixed uniformly spaced grid locations, and the known function values are obtained by measurements at these grid locations. It is well known that the interpolation accuracy of a non-linear space can significantly be increased when the locations of the same number of nodes are optimized for arbitrary locations that are not necessarily restricted to be on regular grid positions. However, the extra computational complexity that is needed to accommodate the arbitrary node locations typically prohibits the use of such scheme in practical applications.
Thus, there is a need for an interpolation method that would be easy to implement and that would provide more flexibility and better performance than the traditional method where the nodes are located at regular grid locations.